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Evaluate [tex]\(\frac{3(x+4)(x+1)}{(x+2)(x-2)}\)[/tex] for [tex]\(x = 4\)[/tex]

A. 10
B. [tex]\(-\frac{10}{3}\)[/tex]
C. [tex]\(\frac{10}{3}\)[/tex]
D. -10


Sagot :

Sure, let's evaluate the given expression step by step for [tex]\(x = 4\)[/tex].

We need to evaluate the expression:
[tex]\[ \frac{3(x+4)(x+1)}{(x+2)(x-2)} \][/tex]
for [tex]\(x = 4\)[/tex].

1. Substitute [tex]\(x = 4\)[/tex] into the expression:
[tex]\[ \frac{3(4+4)(4+1)}{(4+2)(4-2)} \][/tex]

2. Simplify the terms inside the parentheses:
[tex]\[ \frac{3(8)(5)}{(6)(2)} \][/tex]

3. Calculate the values inside the parentheses:
[tex]\[ \frac{3 \cdot 8 \cdot 5}{6 \cdot 2} \][/tex]

4. Simplify the multiplication in the numerator and the denominator:
[tex]\[ \frac{120}{12} \][/tex]

5. Finally, divide the numerator by the denominator:
[tex]\[ 10 \][/tex]

So, the value of the expression [tex]\(\frac{3(x+4)(x+1)}{(x+2)(x-2)}\)[/tex] when [tex]\(x = 4\)[/tex] is [tex]\(\boxed{10}\)[/tex].

The correct answer is A. 10.
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